Question

Find f(5) for this sequence:

f(1) = 2 and f(2) = 5, f(n) = f(1) + f(2) + f(n - 1), for n > 2.

f(5) = ______


Please explain!

Answer 1

f(5) is 10 because 2*1 = 2

Answer 2

Try to find f(4)

Answer 3

f(3)=f(1)+f(2)+f(3-1)=f(1)+f(2)+f(2)=2+5+5=12

Answer 4

what?

Answer 5

You have to find f(3) then f(4) then f(5)

Answer 6

I found f(3) for you and I want you to try to find f(4)

Answer 7

Remember you have f(n)=f(1)+f(2)+f(n-1)

Answer 8

replace the n's with 3's you have
f(3)=f(1)+f(2)+f(3-1)

Answer 9

This means we can find f(3) since we know the values for f(1) and f(2)

Answer 10

f(3)=f(1)+f(2)+f(2)
=2 +5 +5
I replaced f(2) with 5 because your problem says f(2) is 5
I replaced f(1) with 2 because your problem says f(1) is 2

Answer 11

plz explain

Answer 12

Now you can find f(4)
replace all the n's again in f(n)=f(1)+f(2)+f(n-1)
we are going to replace n with 4 this time since we want f(4)
f(n)=f(1)+f(2)+f(n-1)
replace n with 4
f(4)=f(1)+f(2)+f(4-1)
f(4)=f(1)+f(2)+f(3)
f(4)=2 + 5 + 12
f(4)=7+12
f(4)=19

I will leave the last step for you
which is finding f(5)

Answer 13

Have you tried to find f(5) yet?

Answer 14

I still don't understand. :(

Answer 15

how did u know n was 4

Answer 16

n varies
n can equal 3,4,5,6,7,8,9,10, and so on...

Answer 17

f(1) is the first number in the sequence
f(2) is the second number in the sequence
f(3) is the third number in the sequence
f(4) is the fourth number in the sequence
f(5) is the fifth number in the sequence

Answer 18

f(1) and f(2) are given
and f(n)=f(1)+f(2)+f(n-1) equals for every integer n greater than or equal to 3

Answer 19

To find f(3) we need to replace n with 3
so we have
f(3)=f(1)+f(2)+f(3-1)
=f(1)+f(2)+f(2)
=2 +5 +5
=12
So now that you have f(3) you can find f(4) by just replacing the n with 4 now
f(4)=f(1)+f(2)+f(4-1)
=f(1)+f(2)+f(3)
= 2 + 5 +12
=19
Now you can find f(5) just by replacing the n with 5
f(5)=f(1)+f(2)+f(5-1)
you can finish this

Answer 20

f(3)=f(1)+f(2)+f(3-1)
=f(1)+f(2)+f(2)
=2 +5 +5 were did the five come from?
=12